Sometimes a Groebner basis computation doesn't finish quickly enough. If so then this section might be of use. THIS PAGE IS UNDER CONSTRUCTION.
Partially computed Groebner bases
Suppose that you have computed part of a Groebner basis. For example, you may have interrupted the computation using CTRL-C (typing 'c' while holding the CTRL key down, in emacs, you have to type CTRL-C twice), or you may have given options requesting only partial computation.
i1 : R = ZZ/32003[a..e];
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i2 : I = ideal(random(3,R),random(3,R),random(3,R))
3 2 2 3 2
o2 = ideal (4946a + 15130a b + 10667a*b + 13156b + 11207a c + 3599a*b*c +
------------------------------------------------------------------------
2 2 2 3 2 2
6440b c + 7758a*c - 474b*c - 14376c - 840a d - 4011a*b*d - 7106b d +
------------------------------------------------------------------------
2 2 2 2
909a*c*d - 4979b*c*d + 15104c d + 3525a*d + 11153b*d + 6551c*d +
------------------------------------------------------------------------
3 2 2
8468d + 5073a e - 10045a*b*e + 6479b e - 10756a*c*e + 7041b*c*e -
------------------------------------------------------------------------
2 2 2
2450c e + 14408a*d*e + 1525b*d*e - 10569c*d*e - 11993d e + 15231a*e +
------------------------------------------------------------------------
2 2 2 3 3 2
1601b*e - 7985c*e - 6424d*e - 4029e , - 12593a - 13073a b -
------------------------------------------------------------------------
2 3 2 2 2
10694a*b + 2679b + 2430a c + 11183a*b*c + 9817b c - 11848a*c -
------------------------------------------------------------------------
2 3 2 2
11216b*c - 9620c - 945a d - 3984a*b*d - 6958b d + 13776a*c*d +
------------------------------------------------------------------------
2 2 2 2 3
15782b*c*d + 4955c d - 5195a*d - 12435b*d - 15426c*d - 4191d -
------------------------------------------------------------------------
2 2 2
2087a e - 12405a*b*e - 4288b e - 2469a*c*e - 4681b*c*e - 7072c e +
------------------------------------------------------------------------
2 2 2
6201a*d*e + 3701b*d*e - 8496c*d*e - 14127d e + 7974a*e - 8899b*e -
------------------------------------------------------------------------
2 2 3 3 2 2 3
9356c*e - 2783d*e - 68e , - 10405a - 504a b + 6148a*b - 2434b -
------------------------------------------------------------------------
2 2 2 2 3 2
64a c + 829a*b*c + 2008b c + 2416a*c + 11051b*c + 13653c - 2115a d +
------------------------------------------------------------------------
2 2 2
11817a*b*d - 5514b d + 15159a*c*d - 6354b*c*d - 6501c d - 12542a*d +
------------------------------------------------------------------------
2 2 3 2 2
4660b*d + 15279c*d - 13242d + 1271a e + 15465a*b*e + 8134b e +
------------------------------------------------------------------------
2
8757a*c*e - 2959b*c*e + 408c e + 4853a*d*e + 8542b*d*e + 14027c*d*e -
------------------------------------------------------------------------
2 2 2 2 2 3
15505d e + 10444a*e - 7456b*e - 4878c*e + 8476d*e - 13202e )
o2 : Ideal of R
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i3 : gens gb(I,PairLimit=>7);
1 7
o3 : Matrix R <--- R
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Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
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i5 : leadTerm gens g
o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o5 : Matrix R <--- R
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We can make a Groebner basis snapshot by using StopBeforeComputation, or
gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)
o6 = | ab2+9362b3-11651a2c-12986abc-8035b2c-9632ac2+2657bc2-14491c3+3980a2d+
------------------------------------------------------------------------
8773abd+7349b2d-11373acd+9105bcd-15132c2d+8882ad2-14493bd2-877cd2-8425d3
------------------------------------------------------------------------
+7522a2e+8185abe+7661b2e-5667ace+6881bce+8442c2e-12834ade-375bde-6350cde
------------------------------------------------------------------------
-573d2e+4666ae2-2533be2-7146ce2-14044de2+13044e3
------------------------------------------------------------------------
a2b-2563b3+460a2c-2251abc-453b2c-2777ac2-3104bc2+6030c3+5242a2d+3036abd-
------------------------------------------------------------------------
1706b2d+14493acd-4840bcd+7338c2d-4025ad2-13902bd2-2003cd2+11476d3+
------------------------------------------------------------------------
7459a2e+1311abe-3254b2e-5296ace-2579bce-2437c2e-2558ade-8895bde-5392cde-
------------------------------------------------------------------------
13404d2e-10652ae2+5776be2-6936ce2+5927de2-9871e3
------------------------------------------------------------------------
a3-4014b3-6805a2c+14492abc+1524b2c+8616ac2+329bc2-299c3-9556a2d-3595abd+
------------------------------------------------------------------------
9808b2d+10139acd+8989bcd-2763c2d+15099ad2-4701bd2-6448cd2-11272d3+
------------------------------------------------------------------------
5135a2e+9471abe+14695b2e+10219ace+15076bce-11063c2e-1336ade+8556bde-
------------------------------------------------------------------------
1007cde-792d2e-13134ae2+8448be2+15605ce2-15162de2-5488e3
------------------------------------------------------------------------
b3c-12415a2c2+15824abc2+5042b2c2-4186ac3-11802bc3-1918c4-5811b3d+
------------------------------------------------------------------------
4724a2cd-3061abcd-15271b2cd+13309ac2d-6262bc2d+14727c3d-11996a2d2-
------------------------------------------------------------------------
6651abd2-15251b2d2+978acd2+15069bcd2+6255c2d2+13106ad3+7534bd3+5932cd3+
------------------------------------------------------------------------
11661d4-12945b3e+9035a2ce+7343abce+9333b2ce-11655ac2e-11846bc2e-10753c3e
------------------------------------------------------------------------
+14338a2de-2386abde+8897b2de+12884acde+15234bcde-11184c2de+15003ad2e+
------------------------------------------------------------------------
1096bd2e-5919cd2e-607d3e-15048a2e2+10659abe2+15045b2e2+3633ace2-3155bce2
------------------------------------------------------------------------
-8263c2e2-4961ade2+10814bde2+5663cde2+14517d2e2+13751ae3-2515be3-
------------------------------------------------------------------------
15241ce3+6320de3-6050e4
------------------------------------------------------------------------
b4+14441a2c2+4805abc2-522b2c2-764ac3+7405bc3-9205c4+2286b3d+14189a2cd-
------------------------------------------------------------------------
12919abcd-2229b2cd-11619ac2d-6189bc2d+9878c3d-5706a2d2-12590abd2-
------------------------------------------------------------------------
4813b2d2+4913acd2-9229bcd2+13468c2d2-11373ad3+1774bd3-1985cd3+4603d4+
------------------------------------------------------------------------
12296b3e-9222a2ce+12013abce+4731b2ce-2917ac2e+9555bc2e+18c3e-13418a2de-
------------------------------------------------------------------------
4724abde-14299b2de-8450acde-14447bcde-6070c2de+13571ad2e+14560bd2e-
------------------------------------------------------------------------
5759cd2e-13300d3e-14530a2e2+8469abe2-6503b2e2-6210ace2+11262bce2+
------------------------------------------------------------------------
7918c2e2+2226ade2-3012bde2+8837cde2-8021d2e2-7669ae3+537be3+8641ce3-
------------------------------------------------------------------------
6840de3+1190e4 abc3+10050b2c3-8435ac4-8845bc4+8700c5-3957a2c2d+
------------------------------------------------------------------------
15455abc2d-12100b2c2d-6963ac3d+4938bc3d+4587c4d+15436b3d2-5226a2cd2+
------------------------------------------------------------------------
5900abcd2-6562b2cd2+13281ac2d2-15233bc2d2-12263c3d2-412a2d3-14267abd3-
------------------------------------------------------------------------
14229b2d3-5790acd3+9207bcd3+11514c2d3-2145ad4+1085bd4+9331cd4+1815d5+
------------------------------------------------------------------------
379a2c2e+12625abc2e+12988b2c2e+14604ac3e+7694bc3e-13914c4e+8830b3de-
------------------------------------------------------------------------
11284a2cde+222abcde+5230b2cde-14992ac2de-5018bc2de-8282c3de-15436a2d2e+
------------------------------------------------------------------------
4368abd2e+9483b2d2e-9458acd2e-8184bcd2e+12727c2d2e+15810ad3e-5464bd3e+
------------------------------------------------------------------------
8382cd3e-10513d4e-14165b3e2-10890a2ce2-9142abce2+13098b2ce2-8025ac2e2-
------------------------------------------------------------------------
5575bc2e2+3450c3e2-12152a2de2-13439abde2+8957b2de2-7356acde2-2179bcde2+
------------------------------------------------------------------------
15116c2de2+6821ad2e2+6394bd2e2-8250cd2e2-12550d3e2+11468a2e3-9192abe3-
------------------------------------------------------------------------
10316b2e3+15213ace3-2897bce3-11288c2e3+10541ade3+10166bde3-4911cde3-
------------------------------------------------------------------------
8711d2e3+4882ae4+14785be4-9069ce4+10780de4+13379e5
------------------------------------------------------------------------
a2c3-3004b2c3-5292ac4+8766bc4+8355c5-1003a2c2d-5081abc2d+3101b2c2d-
------------------------------------------------------------------------
3252ac3d+2206bc3d+5728c4d-669b3d2-11491a2cd2-2727abcd2-13545b2cd2+
------------------------------------------------------------------------
13722ac2d2+5214bc2d2-15684c3d2-4760a2d3-2934abd3-2149b2d3+12838acd3-
------------------------------------------------------------------------
99bcd3+3478c2d3+4299ad4+4517bd4+15723cd4-6153d5+11654a2c2e+13996abc2e-
------------------------------------------------------------------------
6646b2c2e-14008ac3e-335bc3e-15085c4e-12548b3de-12623a2cde+6628abcde-
------------------------------------------------------------------------
1250b2cde+8472ac2de+13608bc2de-9664c3de+15886a2d2e-10579abd2e-11510b2d2e
------------------------------------------------------------------------
-4513acd2e+348bcd2e-6317c2d2e-10640ad3e-12712bd3e-11226cd3e+6078d4e+
------------------------------------------------------------------------
11468b3e2-5317a2ce2-9064abce2+11680b2ce2+7999ac2e2-14611bc2e2-9399c3e2-
------------------------------------------------------------------------
10594a2de2-6657abde2-903b2de2+5272acde2-10636bcde2-729c2de2-10720ad2e2+
------------------------------------------------------------------------
2862bd2e2+4619cd2e2-12828d3e2-12636a2e3+7405abe3-10203b2e3-1952ace3-
------------------------------------------------------------------------
8400bce3+7477c2e3-6723ade3+15022bde3-12755cde3-4841d2e3+5497ae4+11418be4
------------------------------------------------------------------------
-14160ce4-8772de4+1740e5 |
1 7
o6 : Matrix R <--- R
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i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
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